Athermometer that was used in a calorimeter was consistently 2.7 °c too high. how would this affect the calculations of δh for the reactions conducted in the calorimeter?

The calorimetry experiment is usually done to determine the heat capacity of the sample. The working equation would be:

Q = mCpΔT
Q is the energy
m is the mass of sample
Cp is the heat capacity
ΔT is the temperature

So, if the thermometer is too high, then that would affect ΔT, which would make it greater. Consequently, you would calculate a much lesser heat capacity of the sample compared to the theoretical value.